Mourinho did nothing to diffuse tension between the club and Spain's coach Vicente Del Bosque, whom he had accused of causing Costa's injury problems by over-playing him in two internationals earlier this month.
"He played for the national team and we lost him for four matches in three different competitions," Mourinho told reporters at a news conference.
"Now he is again available but he needs to be under special care. I'm always supportive of players playing for their countries when they are in the condition to do so.
"But I'm nobody to stand in the way of the national team, I can't stop him going away with his country."
Del Bosque had defended the decision to use Costa when he said on Thursday that "in some things we are flexible and in some we are stubborn and in this we are stubborn".
Chelsea's annoyance was compounded by having another of their three senior strikers, Frenchman Loic Remy, unfit as well.
That meant that Didier Drogba, 36, had to play two full games in the space of three days, in the Premier League away to Manchester United on Sunday and then at Shrewsbury in the Capital One (League) Cup.
He scored a crucial goal in each game but Mourinho, who is expected to rest him and bring back Costa against QPR, said it was asking too much of the veteran.
"He was fantastic in the last week when we were without Diego and Remy and in real trouble, doing something nobody should have to do in playing two lots of 90 minutes with 48 hours difference.
"He managed to do that in an absolutely fantastic way."
"It is good for us," the manager added of Costa's return. "It's difficult when you only have one striker available, but when you have two the situation improves."
Remy and midfielder Jon Obi Mikel are unavailable for QPR's visit to the league leaders, who go into the game four points ahead of second-placed Southampton and six clear of champions Manchester City, who do not play until the following day.